On second-order rational difference equations, part 1

References

• Amleh , A.M. , Camouzis , E. and Ladas , G. 2006 . On the boundedness character of rational equations, part 2 . Journal of Difference Equations and Applications , 12 : 637 – 650 .
   Web of Science ®Google Scholar
• Amleh , A.M. , Georgiou , D.A. , Grove , E.A. and Ladas , G. 1999 . On the recursive sequence . Journal of Mathematical Analysis and Applications , 233 : 790 – 798 .
   Web of Science ®Google Scholar
• Barbeau , E. , Gelford , B. and Tanny , S. 1995 . Periodicities of solutions of the generalized Lyness equation . Journal of Difference Equations and Applications , 1 : 291 – 306 .
   Google Scholar
• Bastien , G. and Rogalski , M. 2004 . Global behavior of the solutions of Lyness' difference equation . Journal of Difference Equations and Applications , 11 : 997 – 1003 .
   Google Scholar
• Bastien , G. and Rogalski , M. 2007 . Global behavior of the solutions of the k-lacunary order 2k Lyness' difference equation in and of other more general equations . Journal of Difference Equations and Applications , 13 : 79 – 88 .
   Web of Science ®Google Scholar
• Bellavia , M.R. , Camouzis , E. , Kudlak , Z.A. and Ladas , G. 2007 . On the boundendness character of solutions of rational difference equations, part 3 . Journal of Difference Equations and Applications ,
   Google Scholar
• Berg , L. 2002 . On the asymptotics of nonlinear difference equations . Journal of Analytical and Applied Pyrolysis , 21 : 1061 – 1074 .
   Google Scholar
• Brand , L. 1955 . A sequence defined by a difference equation . The American Mathematical Monthly , 62 : 489 – 492 .
   Google Scholar
• Camouzis , E. 2006 . On the boundedness of some rational difference equations . Journal of Difference Equations and Applications , 12 : 69 – 94 .
   Web of Science ®Google Scholar
• Camouzis , E. and Ladas , G. 2002 . Three trichotomy conjectures . Journal of Difference Equations and Applications , 8 : 495 – 500 .
   Web of Science ®Google Scholar
• Camouzis , E. and Ladas , G. 2006 . When does local stability imply global attractivity in rational equations? . Journal of Difference Equations and Applications , 12 : 863 – 885 .
   Web of Science ®Google Scholar
• Camouzis , E. and Ladas , G. 2006 . When does periodicity destroys boundedness in rational difference equations? . Journal of Difference Equations and Applications , 12 : 961 – 979 .
   Web of Science ®Google Scholar
• Camouzis, E. and Ladas, G., Periodically forced Pielou's Equation (to appear).
   Google Scholar
• Camouzis, E. and Ladas, G., Global convergence on difference equations (to appear).
   Google Scholar
• Camouzis , E. and Ladas , G. 2007 . Dynamics of Third-Order Rational Difference Equations; With Open Problems and Conjectures , Boca Rotan, FL : Chapman & Hall/CRC Press . (to appear in 2007)
   Google Scholar
• Camouzis , E. , Ladas , G. , Palladino , F. and Quinn , E.P. 2006 . On the boundedness character of rational equations, part 1 . Journal of Difference Equations and Applications , 12 : 503 – 523 .
   Web of Science ®Google Scholar
• Camouzis , E. , Ladas , G. and Quinn , E.P. 2005 . On third order rational difference equations, part 6 . Journal of Difference Equations and Applications , 11 : 759 – 777 .
   Web of Science ®Google Scholar
• Cima , A. , Gasull , A. and Manosa , V. 2007 . Dynamics of the third order Lyness' difference equation . Journal of Difference Equations and Applications ,
   Google Scholar
• Csörnyei , M. and Laczkovich , M. 2001 . Some periodic and non-periodic Recursions . Monatshefte für Mathematik , 132 : 215 – 236 .
   Web of Science ®Google Scholar
• Gibbons , C.H. , Kulenovic , M.R.S. and Ladas , G. 2002 . On the recursive sequence . Math Sci Res Hot-Line , 4 ( 2 ) : 1 – 11 .
   Google Scholar
• Gibbons , C.H. , Kulenovic , M.R.S. , Ladas , G. and Voulov , H.D. 2002 . On the trichotomy character of . Journal of Difference Equations and Applications , 8 : 75 – 92 .
   Web of Science ®Google Scholar
• Grove , E.A. , Kostrov , Y. , Ladas , G. and Predescu , M. 2005 . On third-order rational difference equations, part 4 . Journal of Difference Equations and Applications , 11 : 261 – 269 .
   Web of Science ®Google Scholar
• Grove , E.A. , Kostrov , Y. , Ladas , G. and Schultz , S.W. 2007 . Riccati difference equations with real period-2 coefficients . Communications on Applied Nonlinear Analysis , 14 : 33 – 56 .
   Google Scholar
• Grove , E.A. and Ladas , G. 2005 . Periodicities in Nonlinear Difference Equations , Boca Rotan, FL : Chapman and Hall/CRC Press .
   Google Scholar
• Grove , E.A. , Janowski , E.J. , Kent , C.M. and Ladas , G. 1994 . On the rational recursive sequence . Communications on Applied Nonlinear Analysis , 1 : 61 – 72 .
   Google Scholar
• Hoag , J.T. 2004 . Monotonicity of solutions converging to a saddle point equilibrium . Journal of Mathematical Analysis and Applications , 295 : 10 – 14 .
   Web of Science ®Google Scholar
• Huang , Y.S. and Knopf , P.M. 2004 . Boundedness of positive solutions of second order rational difference equations . Journal of Difference Equations and Applications , 10 : 935 – 940 .
   Web of Science ®Google Scholar
• Kalikow, S., Knopf, P.M., Huang, Y.S. and Nyerges, G., Convergence properties in the nonhyperbolic case . Journal of Mathematical Analysis and Applications (to appear).
   Google Scholar
• Karakostas , G.L. and Stevic , S. 2004 . On the recursive sequence . Journal of Difference Equations and Applications , 10 : 809 – 815 .
   Web of Science ®Google Scholar
• Kent , C.M. 2001 . “ Convergence of solutions in a nonhyperbolic case with positive equilibrium ” . In Proceedings of the Third World Congress of Nonlinear Analysts , Vol. 47 , 4651 – 4665 . Amsterdam : Elsevier Science Ltd. . July 19–16, 2000, Catania, Sicily, Italy
   Google Scholar
• Kent , C.M. 2004 . “ Convergence of solutions in a nonhyperbolic case with positive equilibrium ” . In Proceedings of the Sixth International Conference on Difference Equations and Applications: New Progress in Difference Equations , Edited by: Aulbach , B. , Elaydi , S. and Ladas , G. 485 – 492 . Boca Rotan, FL : Chapman & Hall/CRC . August 2001, Augburg, Germany
   Google Scholar
• Kocic , V.L. and Ladas , G. 1993 . Global Behavior of Nonlinear Difference Equations of Higher Order with Applications , Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Kocic , V.L. , Ladas , G. and Rodrigues , I.W. 1993 . On rational recursive sequences . Journal of Mathematical Analysis and Applications , 173 : 127 – 157 .
   Web of Science ®Google Scholar
• Kosmala , W.A. , Kulenović , M.R.S. , Ladas , G. and Teixeira , C.T. 2000 . On the recursive sequence . Journal of Mathematical Analysis and Applications , 251 : 571 – 586 .
   Web of Science ®Google Scholar
• Kulenović , M.R.S. 2000 . Invariants and related Liapunov functions for difference equations . Applied Mathematics Letters , 13 : 1 – 8 .
   Web of Science ®Google Scholar
• Kulenović , M.R.S. and Ladas , G. 2001 . Dynamics of Second Order Rational Difference Equations; With Open Problems and Conjectures , Boca Rotan, FL : Chapman & Hall/CRC Press .
   Google Scholar
• Kulenović , M.R.S. , Ladas , G. and Prokup , N.R. 2000 . On the recursive sequence . Journal of Difference Equations and Applications , 5 : 563 – 576 .
   Google Scholar
• Kulenović , M.R.S. , Ladas , G. and Prokup , N.R. 2001 . A rational difference equation . Computers and Mathematics with Applications , 41 : 671 – 678 .
   Web of Science ®Google Scholar
• Kulenović , M.R.S. , Ladas , G. and Sizer , W.S. 1998 . On the recursive sequence . Mathematical Sciences Research Hot-Line , 2 ( 5 ) : 1 – 16 .
   Google Scholar
• Kulenović, M.R.S. and Merino, O., Stability analysis of Pielou's equation with period-two coefficient. Journal of Difference Equations and Applications, (to appear)
   Google Scholar
• Kulenović , M.R.S. and Merino , O. 2006 . Global attractivity of the equation for q < p . Journal of Difference Equations and Applications , 12 : 101 – 108 .
   Web of Science ®Google Scholar
• Kuruklis , S.A. and Ladas , G. 1992 . Oscillation and global attractivity in a discrete delay logistic model . Quarterly of Applied Mathematics , L : 227 – 233 .
   Web of Science ®Google Scholar
• Ladas , G. 2004 . On third-order rational difference equations, part 1 . Journal of Difference Equations and Applications , 10 : 869 – 879 .
   Web of Science ®Google Scholar
• Ladas , G. 1995 . On the recursive sequence . Journal of Difference Equations and Applications , 1 : 317 – 321 .
   Google Scholar
• Ladas , G. , Tzanetopoulos , G. and Thomas , E. 1995 . On the stability of Lyness's Equation . Dynamics of Continuous, Discrete and Impulsive Systems , 1 : 245 – 254 .
   Google Scholar
• Lyness , R.C. 1942 . Note 1581 . The Mathematical Gazette , 26 : 62
   Google Scholar
• Lyness , R.C. 1945 . Note 1847 . The Mathematical Gazette , 29 : 231
   Google Scholar
• Nussbaum , R. 2007 . Global stability, two conjectures and maple . Nonlinear Analysis , 66 : 1064 – 1090 .
   Web of Science ®Google Scholar
• Philos , Ch.G. , Purnaras , I.K. and Sficas , Y.G. 1994 . Global attractivity in a nonlinear difference equation . Applied Mathematics and Computation , 62 : 249 – 258 .
   Web of Science ®Google Scholar
• Sizer , W.S. 2003 . Periodicity in the Lyness equation . Mathematical Sciences Research Journal , 7 : 366 – 372 .
   Google Scholar
• Sizer , W.S. 2000 . “ Some periodic solutions of the Lyness equation ” . In Proceedings of the Fifth International Conference on Difference Equations and Applications , London : Gordon and Breach Science Publishers . January 3–7, Temuca, Chile
   Google Scholar
• Stevic , S. 2007 . On the recursive sequence . Journal of Difference Equations and Applications , 13 : 41 – 46 .
   Web of Science ®Google Scholar
• Taixiang , S. 2005 . On non-oscillatory solution of the recursive sequence . Journal of Difference Equations and Applications , 11 : 483 – 485 .
   Web of Science ®Google Scholar
• Taixiang , S. and Hongjian , X. 2005 . On the solutions of a class of difference equations . Journal of Mathematical Analysis and Applications , 311 : 766 – 770 .
   Google Scholar
• Taixiang , S. and Hongjian , X. 2007 . On convergence of the solutions of the difference equation . Journal of Mathematical Analysis and Applications , 325 : 1491 – 1494 .
   Google Scholar
• Zeeman, E.C., Geometric unfolding of a difference equation. http://www.math.utsa.edu/ecz/gu.html
   Google Scholar